In this paper, we give important properties as completeness, completion and precompactness of Hausdorff intuitionistic fuzzy metric spaces which is given by Gregori et al [13] and establish the precise relationship between the Hausdorff metric of a metric space (X, d) and the Hausdorff intuitionistic fuzzy metric of the standart intuitionistic fuzzy metric of d, and give two examples. AMS Subje...

This paper defines and discusses the Hausdorff metric on the space of nonempty, closed, and bounded subsets of a given metric space. We consider two important topological properties, completeness and total boundedness. We prove that each of these properties is posessed by a Hausdorff metric space if the property is possesed by the underlying metric space. Finally, we explore applications of the...

We introduce Lipschitz continuity of set-valued maps with respect to a given set difference. The existence of Lipschitz selections that pass through any point of the graph of the map and inherit its Lipschitz constant is studied. We show that the Lipschitz property of the set-valued map with respect to the Demyanov difference with a given constant is characterized by the same property of its ge...

In this paper we establish an alternative characterization of the completion theory for metric spaces which makes fundamental use of a special type of real valued maps, and we derive alternative descriptions for the completions of both Hausdorff uniform and Hausdorff uniform approach spaces. Mathematics Subject Classifications (2000): 54B30, 54D35, 54E15, 54E35, 54E99.

Let Y be a proximinal subspace of finite codimension of c0. We show that Y is proximinal in ∞ and the metric projection from ∞ onto Y is Hausdorff metric continuous. In particular, this implies that the metric projection from ∞ onto Y is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous.

In this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.  

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

In this work the main objective is to extend the theory of Hausdorff measures in general metric spaces. Throughout the thesis Hausdorff measures are defined using premeasures. A condition on premeasures of ‘finite order’ is introduced which enables the use of a Vitali type covering theorem. Weighted Hausdorff measures are shown to be an important tool when working with Hausdorff measures define...